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<h2>区域</h2>
<p><a href="#section_list">List of Operators ↓</a></p>
<p>This chapter describes operators of region morphology.
</p>
<h3>Concept of Region Morphology</h3>
<p>Region morphology provides a set of morphological operators that allow to
modify or describe the shape of a region.
The morphological operators can be used, for example, to connect or
disconnect adjacent regions or to smooth the boundary of a region.
In the following, we will take a closer look at the morphological
operators.
</p>
<h3>Dilation and Erosion</h3>
<p>To dilate or erode an input region, a structuring element is applied
to the input region. This structuring element is scanned over the
image line-by-line. During dilation the reference point of the
structuring element is added to the resulting region whenever the
structuring element and the input region have at least one pixel in
common. This results in an enlarged region, as shown in the image
below. Erosion reduces the area of the input region because the
reference point is only added to the resulting region if the structuring
element lies completely within the input region. As a result, erosion can
alternatively be used to find objects.
</p>
<div style="text-align:center;" class="figure">
<table style="margin-left:auto;margin-right:auto">
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</tr>
<tr>
<td align="center">
        (
      1)
    </td>
<td align="center">
        (
      2)
    </td>
<td align="center">
        (
      3)
    </td>
<td align="center">
        (
      4)
    </td>
</tr>
</table>
<div style="margin-bottom:30px;text-align:center;" class="caption">
(1) Image with input region,
(2) structuring element with reference point in the origin,
(3) result of dilating the input region,
(4) result of eroding the input region.
</div>
</div>
<p>These operators can be used to dilate or erode a region:
</p>
<div style="text-align:center"><table style="margin-left:auto;margin-right:auto" class="table">
<col span="1">
<col span="1">
<col span="1">
<col span="1">
<tr>
<th style="text-align:left">
Morphological Operators </th>
<th style="text-align:left">  </th>
<th style="text-align:left">Structuring Element </th>
<th style="text-align:left">Reference Point </th>
</tr>
<tr>
<td style="text-align:left">
<a href="dilation1.html"><code><span data-if="hdevelop" style="display:inline"><code>dilation1</code></span><span data-if="c" style="display:none"><code>dilation1</code></span><span data-if="cpp" style="display:none"><code>Dilation1</code></span><span data-if="com" style="display:none"><code>Dilation1</code></span><span data-if="dotnet" style="display:none"><code>Dilation1</code></span><span data-if="python" style="display:none"><code>dilation1</code></span></code></a> </td>
<td style="text-align:left">
<a href="erosion1.html"><code><span data-if="hdevelop" style="display:inline"><code>erosion1</code></span><span data-if="c" style="display:none"><code>erosion1</code></span><span data-if="cpp" style="display:none"><code>Erosion1</code></span><span data-if="com" style="display:none"><code>Erosion1</code></span><span data-if="dotnet" style="display:none"><code>Erosion1</code></span><span data-if="python" style="display:none"><code>erosion1</code></span></code></a> </td>
<td style="text-align:left">arbitrary </td>
<td style="text-align:left">origin </td>
</tr>
<tr>
<td style="text-align:left">
<a href="minkowski_add1.html"><code><span data-if="hdevelop" style="display:inline"><code>minkowski_add1</code></span><span data-if="c" style="display:none"><code>minkowski_add1</code></span><span data-if="cpp" style="display:none"><code>MinkowskiAdd1</code></span><span data-if="com" style="display:none"><code>MinkowskiAdd1</code></span><span data-if="dotnet" style="display:none"><code>MinkowskiAdd1</code></span><span data-if="python" style="display:none"><code>minkowski_add1</code></span></code></a> </td>
<td style="text-align:left">
<a href="minkowski_sub1.html"><code><span data-if="hdevelop" style="display:inline"><code>minkowski_sub1</code></span><span data-if="c" style="display:none"><code>minkowski_sub1</code></span><span data-if="cpp" style="display:none"><code>MinkowskiSub1</code></span><span data-if="com" style="display:none"><code>MinkowskiSub1</code></span><span data-if="dotnet" style="display:none"><code>MinkowskiSub1</code></span><span data-if="python" style="display:none"><code>minkowski_sub1</code></span></code></a> </td>
<td style="text-align:left">arbitrary, transposed </td>
<td style="text-align:left">origin </td>
</tr>
<tr>
<td style="text-align:left">
<a href="dilation2.html"><code><span data-if="hdevelop" style="display:inline"><code>dilation2</code></span><span data-if="c" style="display:none"><code>dilation2</code></span><span data-if="cpp" style="display:none"><code>Dilation2</code></span><span data-if="com" style="display:none"><code>Dilation2</code></span><span data-if="dotnet" style="display:none"><code>Dilation2</code></span><span data-if="python" style="display:none"><code>dilation2</code></span></code></a> </td>
<td style="text-align:left">
<a href="erosion2.html"><code><span data-if="hdevelop" style="display:inline"><code>erosion2</code></span><span data-if="c" style="display:none"><code>erosion2</code></span><span data-if="cpp" style="display:none"><code>Erosion2</code></span><span data-if="com" style="display:none"><code>Erosion2</code></span><span data-if="dotnet" style="display:none"><code>Erosion2</code></span><span data-if="python" style="display:none"><code>erosion2</code></span></code></a> </td>
<td style="text-align:left">arbitrary </td>
<td style="text-align:left">arbitrary </td>
</tr>
<tr>
<td style="text-align:left">
<a href="minkowski_add2.html"><code><span data-if="hdevelop" style="display:inline"><code>minkowski_add2</code></span><span data-if="c" style="display:none"><code>minkowski_add2</code></span><span data-if="cpp" style="display:none"><code>MinkowskiAdd2</code></span><span data-if="com" style="display:none"><code>MinkowskiAdd2</code></span><span data-if="dotnet" style="display:none"><code>MinkowskiAdd2</code></span><span data-if="python" style="display:none"><code>minkowski_add2</code></span></code></a> </td>
<td style="text-align:left">
<a href="minkowski_sub2.html"><code><span data-if="hdevelop" style="display:inline"><code>minkowski_sub2</code></span><span data-if="c" style="display:none"><code>minkowski_sub2</code></span><span data-if="cpp" style="display:none"><code>MinkowskiSub2</code></span><span data-if="com" style="display:none"><code>MinkowskiSub2</code></span><span data-if="dotnet" style="display:none"><code>MinkowskiSub2</code></span><span data-if="python" style="display:none"><code>minkowski_sub2</code></span></code></a> </td>
<td style="text-align:left">arbitrary, transposed </td>
<td style="text-align:left">arbitrary </td>
</tr>
<tr>
<td style="text-align:left">
<a href="dilation_circle.html"><code><span data-if="hdevelop" style="display:inline"><code>dilation_circle</code></span><span data-if="c" style="display:none"><code>dilation_circle</code></span><span data-if="cpp" style="display:none"><code>DilationCircle</code></span><span data-if="com" style="display:none"><code>DilationCircle</code></span><span data-if="dotnet" style="display:none"><code>DilationCircle</code></span><span data-if="python" style="display:none"><code>dilation_circle</code></span></code></a> </td>
<td style="text-align:left">
<a href="erosion_circle.html"><code><span data-if="hdevelop" style="display:inline"><code>erosion_circle</code></span><span data-if="c" style="display:none"><code>erosion_circle</code></span><span data-if="cpp" style="display:none"><code>ErosionCircle</code></span><span data-if="com" style="display:none"><code>ErosionCircle</code></span><span data-if="dotnet" style="display:none"><code>ErosionCircle</code></span><span data-if="python" style="display:none"><code>erosion_circle</code></span></code></a> </td>
<td style="text-align:left">circular </td>
<td style="text-align:left">origin </td>
</tr>
<tr>
<td style="text-align:left">
<a href="dilation_rectangle1.html"><code><span data-if="hdevelop" style="display:inline"><code>dilation_rectangle1</code></span><span data-if="c" style="display:none"><code>dilation_rectangle1</code></span><span data-if="cpp" style="display:none"><code>DilationRectangle1</code></span><span data-if="com" style="display:none"><code>DilationRectangle1</code></span><span data-if="dotnet" style="display:none"><code>DilationRectangle1</code></span><span data-if="python" style="display:none"><code>dilation_rectangle1</code></span></code></a> </td>
<td style="text-align:left">
<a href="erosion_rectangle1.html"><code><span data-if="hdevelop" style="display:inline"><code>erosion_rectangle1</code></span><span data-if="c" style="display:none"><code>erosion_rectangle1</code></span><span data-if="cpp" style="display:none"><code>ErosionRectangle1</code></span><span data-if="com" style="display:none"><code>ErosionRectangle1</code></span><span data-if="dotnet" style="display:none"><code>ErosionRectangle1</code></span><span data-if="python" style="display:none"><code>erosion_rectangle1</code></span></code></a> </td>
<td style="text-align:left">rectangular </td>
<td style="text-align:left">origin
</td>
</tr>
</table></div>
<p>Note that Minkowski addition and dilation are identical if
the structuring element is symmetric. The same applies to Minkowski
subtraction and erosion. Erosion can be used to separate objects
that are attached to each other. In the following, the steps that are
required to separate objects are described briefly.
</p>
<p>First, the objects of the image must be segmented, for example by
using 该算子 <a href="threshold.html"><code><span data-if="hdevelop" style="display:inline"><code>threshold</code></span><span data-if="c" style="display:none"><code>threshold</code></span><span data-if="cpp" style="display:none"><code>Threshold</code></span><span data-if="com" style="display:none"><code>Threshold</code></span><span data-if="dotnet" style="display:none"><code>Threshold</code></span><span data-if="python" style="display:none"><code>threshold</code></span></code></a>. Next, 该算子
<a href="connection.html"><code><span data-if="hdevelop" style="display:inline"><code>connection</code></span><span data-if="c" style="display:none"><code>connection</code></span><span data-if="cpp" style="display:none"><code>Connection</code></span><span data-if="com" style="display:none"><code>Connection</code></span><span data-if="dotnet" style="display:none"><code>Connection</code></span><span data-if="python" style="display:none"><code>connection</code></span></code></a> is used to get multiple regions instead of a
single region. As you can see in the image (3) below, the result of
the connection is unsatisfactory because several objects are merged.
</p>
<div style="text-align:center;" class="figure">
<table style="margin-left:auto;margin-right:auto">
<tr>
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</g>
</svg></td>
</tr>
<tr>
<td align="center">
        (
      1)
    </td>
<td align="center">
        (
      2)
    </td>
<td align="center">
        (
      3)
    </td>
</tr>
</table>
<div style="margin-bottom:30px;text-align:center;" class="caption">
(1) Image with globular objects,
(2) segmented regions,
(3) connected components.
</div>
</div>
<p>This problem can be solved using erosion. As mentioned above,
erosion reduces the area of the input region. Thus, if erosion
is applied prior to 该算子 <a href="connection.html"><code><span data-if="hdevelop" style="display:inline"><code>connection</code></span><span data-if="c" style="display:none"><code>connection</code></span><span data-if="cpp" style="display:none"><code>Connection</code></span><span data-if="com" style="display:none"><code>Connection</code></span><span data-if="dotnet" style="display:none"><code>Connection</code></span><span data-if="python" style="display:none"><code>connection</code></span></code></a>, the regions
are separated as desired. Lastly, dilation is applied on the
separated regions to approximately get the original shape back.
</p>
<div style="text-align:center;" class="figure">
<table style="margin-left:auto;margin-right:auto">
<tr>
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</g>
</svg></td>
</tr>
<tr>
<td align="center">
        (
      1)
    </td>
<td align="center">
        (
      2)
    </td>
<td align="center">
        (
      3)
    </td>
</tr>
</table>
<div style="margin-bottom:30px;text-align:center;" class="caption">
(1) Segmented regions after erosion,
(2) connected components,
(3) connected components after dilation.
</div>
</div>
<h3>Opening and Closing</h3>
<p>Both operations generate the resulting region by combining dilation
and erosion operations. Opening is an erosion followed by a dilation.
It is useful to eliminate small unwanted structures.
Closing is the opposite of opening, i.e., a dilation followed by
an erosion. The closing operator is able to close small
gaps, as shown below.
</p>
<div style="text-align:center;" class="figure">
<table style="margin-left:auto;margin-right:auto">
<tr>
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</tr>
<tr>
<td align="center">
        (
      1)
    </td>
<td align="center">
        (
      2)
    </td>
<td align="center">
        (
      3)
    </td>
<td align="center">
        (
      4)
    </td>
</tr>
</table>
<div style="margin-bottom:30px;text-align:center;" class="caption">
(1) Image with input region,
(2) structuring element with reference point,
(3) result of applying an opening to the input region,
(4) result of applying a closing.
</div>
</div>
<p>These operators can be used to open or close a region:
</p>
<div style="text-align:center"><table style="margin-left:auto;margin-right:auto" class="table">
<col span="1">
<col span="1">
<col span="1">
<col span="1">
<tr>
<th style="text-align:left">
Morphological Operators </th>
<th style="text-align:left">  </th>
<th style="text-align:left">Structuring Element </th>
<th style="text-align:left">Reference Point </th>
</tr>
<tr>
<td style="text-align:left">
<a href="opening.html"><code><span data-if="hdevelop" style="display:inline"><code>opening</code></span><span data-if="c" style="display:none"><code>opening</code></span><span data-if="cpp" style="display:none"><code>Opening</code></span><span data-if="com" style="display:none"><code>Opening</code></span><span data-if="dotnet" style="display:none"><code>Opening</code></span><span data-if="python" style="display:none"><code>opening</code></span></code></a> </td>
<td style="text-align:left">
<a href="closing.html"><code><span data-if="hdevelop" style="display:inline"><code>closing</code></span><span data-if="c" style="display:none"><code>closing</code></span><span data-if="cpp" style="display:none"><code>Closing</code></span><span data-if="com" style="display:none"><code>Closing</code></span><span data-if="dotnet" style="display:none"><code>Closing</code></span><span data-if="python" style="display:none"><code>closing</code></span></code></a> </td>
<td style="text-align:left">arbitrary </td>
<td style="text-align:left">origin </td>
</tr>
<tr>
<td style="text-align:left">
<a href="opening_circle.html"><code><span data-if="hdevelop" style="display:inline"><code>opening_circle</code></span><span data-if="c" style="display:none"><code>opening_circle</code></span><span data-if="cpp" style="display:none"><code>OpeningCircle</code></span><span data-if="com" style="display:none"><code>OpeningCircle</code></span><span data-if="dotnet" style="display:none"><code>OpeningCircle</code></span><span data-if="python" style="display:none"><code>opening_circle</code></span></code></a> </td>
<td style="text-align:left">
<a href="closing_circle.html"><code><span data-if="hdevelop" style="display:inline"><code>closing_circle</code></span><span data-if="c" style="display:none"><code>closing_circle</code></span><span data-if="cpp" style="display:none"><code>ClosingCircle</code></span><span data-if="com" style="display:none"><code>ClosingCircle</code></span><span data-if="dotnet" style="display:none"><code>ClosingCircle</code></span><span data-if="python" style="display:none"><code>closing_circle</code></span></code></a> </td>
<td style="text-align:left">circular </td>
<td style="text-align:left">origin </td>
</tr>
<tr>
<td style="text-align:left">
<a href="opening_rectangle1.html"><code><span data-if="hdevelop" style="display:inline"><code>opening_rectangle1</code></span><span data-if="c" style="display:none"><code>opening_rectangle1</code></span><span data-if="cpp" style="display:none"><code>OpeningRectangle1</code></span><span data-if="com" style="display:none"><code>OpeningRectangle1</code></span><span data-if="dotnet" style="display:none"><code>OpeningRectangle1</code></span><span data-if="python" style="display:none"><code>opening_rectangle1</code></span></code></a> </td>
<td style="text-align:left">
<a href="closing_rectangle1.html"><code><span data-if="hdevelop" style="display:inline"><code>closing_rectangle1</code></span><span data-if="c" style="display:none"><code>closing_rectangle1</code></span><span data-if="cpp" style="display:none"><code>ClosingRectangle1</code></span><span data-if="com" style="display:none"><code>ClosingRectangle1</code></span><span data-if="dotnet" style="display:none"><code>ClosingRectangle1</code></span><span data-if="python" style="display:none"><code>closing_rectangle1</code></span></code></a> </td>
<td style="text-align:left">rectangular </td>
<td style="text-align:left">origin
</td>
</tr>
</table></div>
<h3>Further Operators</h3>
<p>In addition to 该算子s mentioned above, you can use
<a href="top_hat.html"><code><span data-if="hdevelop" style="display:inline"><code>top_hat</code></span><span data-if="c" style="display:none"><code>top_hat</code></span><span data-if="cpp" style="display:none"><code>TopHat</code></span><span data-if="com" style="display:none"><code>TopHat</code></span><span data-if="dotnet" style="display:none"><code>TopHat</code></span><span data-if="python" style="display:none"><code>top_hat</code></span></code></a> to get the difference between the input region and
the result of the opening, or <a href="bottom_hat.html"><code><span data-if="hdevelop" style="display:inline"><code>bottom_hat</code></span><span data-if="c" style="display:none"><code>bottom_hat</code></span><span data-if="cpp" style="display:none"><code>BottomHat</code></span><span data-if="com" style="display:none"><code>BottomHat</code></span><span data-if="dotnet" style="display:none"><code>BottomHat</code></span><span data-if="python" style="display:none"><code>bottom_hat</code></span></code></a> to get the
difference between the result of the closing and the input region.
Furthermore, you can calculate the boundary of a region
with 该算子 <a href="boundary.html"><code><span data-if="hdevelop" style="display:inline"><code>boundary</code></span><span data-if="c" style="display:none"><code>boundary</code></span><span data-if="cpp" style="display:none"><code>Boundary</code></span><span data-if="com" style="display:none"><code>Boundary</code></span><span data-if="dotnet" style="display:none"><code>Boundary</code></span><span data-if="python" style="display:none"><code>boundary</code></span></code></a>.
</p>
<div style="text-align:center;" class="figure">
<table style="margin-left:auto;margin-right:auto">
<tr>
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</g>
</svg></td>
</tr>
<tr>
<td align="center">
        (
      1)
    </td>
<td align="center">
        (
      2)
    </td>
<td align="center">
        (
      3)
    </td>
</tr>
</table>
<div style="margin-bottom:30px;text-align:center;" class="caption">
(1) Top hat,
(2) bottom hat,
(3) boundary.
</div>
</div>
<p>该算子 <a href="hit_or_miss.html"><code><span data-if="hdevelop" style="display:inline"><code>hit_or_miss</code></span><span data-if="c" style="display:none"><code>hit_or_miss</code></span><span data-if="cpp" style="display:none"><code>HitOrMiss</code></span><span data-if="com" style="display:none"><code>HitOrMiss</code></span><span data-if="dotnet" style="display:none"><code>HitOrMiss</code></span><span data-if="python" style="display:none"><code>hit_or_miss</code></span></code></a> can be used to find objects, taking
the foreground and the background of the image into account.
To remove unwanted branches from a skeleton, <a href="pruning.html"><code><span data-if="hdevelop" style="display:inline"><code>pruning</code></span><span data-if="c" style="display:none"><code>pruning</code></span><span data-if="cpp" style="display:none"><code>Pruning</code></span><span data-if="com" style="display:none"><code>Pruning</code></span><span data-if="dotnet" style="display:none"><code>Pruning</code></span><span data-if="python" style="display:none"><code>pruning</code></span></code></a>
is a suitable operator.
</p>
<h3>Glossary</h3>
<p>In the following list, the most important terms that are used in the
context of Morphology are described.
</p>
<dl class="generic">


<dt><b>input region</b></dt>
<dd>
<p>
 Region which is modified by morphological
operators.
</p>
</dd>

<dt><b>structuring element</b></dt>
<dd>
<p>
 Region which is used to scan the input
region.
</p>
</dd>
</dl>
<hr>
<h4 id="section_list">算子列表</h4>
<dl>
<dt><a href="bottom_hat.html"><code><span data-if="hdevelop" style="display:inline;">bottom_hat</span><span data-if="dotnet" style="display:none;">BottomHat</span><span data-if="python" style="display:none;">bottom_hat</span><span data-if="cpp" style="display:none;">BottomHat</span><span data-if="c" style="display:none;">bottom_hat</span></code></a></dt>
<dd>Compute the bottom hat of regions.</dd>
</dl>
<dl>
<dt><a href="boundary.html"><code><span data-if="hdevelop" style="display:inline;">boundary</span><span data-if="dotnet" style="display:none;">Boundary</span><span data-if="python" style="display:none;">boundary</span><span data-if="cpp" style="display:none;">Boundary</span><span data-if="c" style="display:none;">boundary</span></code></a></dt>
<dd>Reduce a region to its boundary.</dd>
</dl>
<dl>
<dt><a href="closing.html"><code><span data-if="hdevelop" style="display:inline;">closing</span><span data-if="dotnet" style="display:none;">Closing</span><span data-if="python" style="display:none;">closing</span><span data-if="cpp" style="display:none;">Closing</span><span data-if="c" style="display:none;">closing</span></code></a></dt>
<dd>Close a region.</dd>
</dl>
<dl>
<dt><a href="closing_circle.html"><code><span data-if="hdevelop" style="display:inline;">closing_circle</span><span data-if="dotnet" style="display:none;">ClosingCircle</span><span data-if="python" style="display:none;">closing_circle</span><span data-if="cpp" style="display:none;">ClosingCircle</span><span data-if="c" style="display:none;">closing_circle</span></code></a></dt>
<dd>Close a region with a circular structuring element.</dd>
</dl>
<dl>
<dt><a href="closing_rectangle1.html"><code><span data-if="hdevelop" style="display:inline;">closing_rectangle1</span><span data-if="dotnet" style="display:none;">ClosingRectangle1</span><span data-if="python" style="display:none;">closing_rectangle1</span><span data-if="cpp" style="display:none;">ClosingRectangle1</span><span data-if="c" style="display:none;">closing_rectangle1</span></code></a></dt>
<dd>Close a region with a rectangular structuring element.</dd>
</dl>
<dl>
<dt><a href="dilation1.html"><code><span data-if="hdevelop" style="display:inline;">dilation1</span><span data-if="dotnet" style="display:none;">Dilation1</span><span data-if="python" style="display:none;">dilation1</span><span data-if="cpp" style="display:none;">Dilation1</span><span data-if="c" style="display:none;">dilation1</span></code></a></dt>
<dd>Dilate a region.</dd>
</dl>
<dl>
<dt><a href="dilation2.html"><code><span data-if="hdevelop" style="display:inline;">dilation2</span><span data-if="dotnet" style="display:none;">Dilation2</span><span data-if="python" style="display:none;">dilation2</span><span data-if="cpp" style="display:none;">Dilation2</span><span data-if="c" style="display:none;">dilation2</span></code></a></dt>
<dd>Dilate a region (using a reference point).</dd>
</dl>
<dl>
<dt><a href="dilation_circle.html"><code><span data-if="hdevelop" style="display:inline;">dilation_circle</span><span data-if="dotnet" style="display:none;">DilationCircle</span><span data-if="python" style="display:none;">dilation_circle</span><span data-if="cpp" style="display:none;">DilationCircle</span><span data-if="c" style="display:none;">dilation_circle</span></code></a></dt>
<dd>Dilate a region with a circular structuring element.</dd>
</dl>
<dl>
<dt><a href="dilation_rectangle1.html"><code><span data-if="hdevelop" style="display:inline;">dilation_rectangle1</span><span data-if="dotnet" style="display:none;">DilationRectangle1</span><span data-if="python" style="display:none;">dilation_rectangle1</span><span data-if="cpp" style="display:none;">DilationRectangle1</span><span data-if="c" style="display:none;">dilation_rectangle1</span></code></a></dt>
<dd>Dilate a region with a rectangular structuring element.</dd>
</dl>
<dl>
<dt><a href="erosion1.html"><code><span data-if="hdevelop" style="display:inline;">erosion1</span><span data-if="dotnet" style="display:none;">Erosion1</span><span data-if="python" style="display:none;">erosion1</span><span data-if="cpp" style="display:none;">Erosion1</span><span data-if="c" style="display:none;">erosion1</span></code></a></dt>
<dd>Erode a region.</dd>
</dl>
<dl>
<dt><a href="erosion2.html"><code><span data-if="hdevelop" style="display:inline;">erosion2</span><span data-if="dotnet" style="display:none;">Erosion2</span><span data-if="python" style="display:none;">erosion2</span><span data-if="cpp" style="display:none;">Erosion2</span><span data-if="c" style="display:none;">erosion2</span></code></a></dt>
<dd>Erode a region (using a reference point).</dd>
</dl>
<dl>
<dt><a href="erosion_circle.html"><code><span data-if="hdevelop" style="display:inline;">erosion_circle</span><span data-if="dotnet" style="display:none;">ErosionCircle</span><span data-if="python" style="display:none;">erosion_circle</span><span data-if="cpp" style="display:none;">ErosionCircle</span><span data-if="c" style="display:none;">erosion_circle</span></code></a></dt>
<dd>Erode a region with a circular structuring element.</dd>
</dl>
<dl>
<dt><a href="erosion_rectangle1.html"><code><span data-if="hdevelop" style="display:inline;">erosion_rectangle1</span><span data-if="dotnet" style="display:none;">ErosionRectangle1</span><span data-if="python" style="display:none;">erosion_rectangle1</span><span data-if="cpp" style="display:none;">ErosionRectangle1</span><span data-if="c" style="display:none;">erosion_rectangle1</span></code></a></dt>
<dd>Erode a region with a rectangular structuring element.</dd>
</dl>
<dl>
<dt><a href="hit_or_miss.html"><code><span data-if="hdevelop" style="display:inline;">hit_or_miss</span><span data-if="dotnet" style="display:none;">HitOrMiss</span><span data-if="python" style="display:none;">hit_or_miss</span><span data-if="cpp" style="display:none;">HitOrMiss</span><span data-if="c" style="display:none;">hit_or_miss</span></code></a></dt>
<dd>Hit-or-miss operation for regions.</dd>
</dl>
<dl>
<dt><a href="minkowski_add1.html"><code><span data-if="hdevelop" style="display:inline;">minkowski_add1</span><span data-if="dotnet" style="display:none;">MinkowskiAdd1</span><span data-if="python" style="display:none;">minkowski_add1</span><span data-if="cpp" style="display:none;">MinkowskiAdd1</span><span data-if="c" style="display:none;">minkowski_add1</span></code></a></dt>
<dd>Perform a Minkowski addition on a region.</dd>
</dl>
<dl>
<dt><a href="minkowski_add2.html"><code><span data-if="hdevelop" style="display:inline;">minkowski_add2</span><span data-if="dotnet" style="display:none;">MinkowskiAdd2</span><span data-if="python" style="display:none;">minkowski_add2</span><span data-if="cpp" style="display:none;">MinkowskiAdd2</span><span data-if="c" style="display:none;">minkowski_add2</span></code></a></dt>
<dd>Dilate a region (using a reference point).</dd>
</dl>
<dl>
<dt><a href="minkowski_sub1.html"><code><span data-if="hdevelop" style="display:inline;">minkowski_sub1</span><span data-if="dotnet" style="display:none;">MinkowskiSub1</span><span data-if="python" style="display:none;">minkowski_sub1</span><span data-if="cpp" style="display:none;">MinkowskiSub1</span><span data-if="c" style="display:none;">minkowski_sub1</span></code></a></dt>
<dd>Erode a region.</dd>
</dl>
<dl>
<dt><a href="minkowski_sub2.html"><code><span data-if="hdevelop" style="display:inline;">minkowski_sub2</span><span data-if="dotnet" style="display:none;">MinkowskiSub2</span><span data-if="python" style="display:none;">minkowski_sub2</span><span data-if="cpp" style="display:none;">MinkowskiSub2</span><span data-if="c" style="display:none;">minkowski_sub2</span></code></a></dt>
<dd>Erode a region (using a reference point).</dd>
</dl>
<dl>
<dt><a href="opening.html"><code><span data-if="hdevelop" style="display:inline;">opening</span><span data-if="dotnet" style="display:none;">Opening</span><span data-if="python" style="display:none;">opening</span><span data-if="cpp" style="display:none;">Opening</span><span data-if="c" style="display:none;">opening</span></code></a></dt>
<dd>Open a region.</dd>
</dl>
<dl>
<dt><a href="opening_circle.html"><code><span data-if="hdevelop" style="display:inline;">opening_circle</span><span data-if="dotnet" style="display:none;">OpeningCircle</span><span data-if="python" style="display:none;">opening_circle</span><span data-if="cpp" style="display:none;">OpeningCircle</span><span data-if="c" style="display:none;">opening_circle</span></code></a></dt>
<dd>Open a region with a circular structuring element.</dd>
</dl>
<dl>
<dt><a href="opening_rectangle1.html"><code><span data-if="hdevelop" style="display:inline;">opening_rectangle1</span><span data-if="dotnet" style="display:none;">OpeningRectangle1</span><span data-if="python" style="display:none;">opening_rectangle1</span><span data-if="cpp" style="display:none;">OpeningRectangle1</span><span data-if="c" style="display:none;">opening_rectangle1</span></code></a></dt>
<dd>Open a region with a rectangular structuring element.</dd>
</dl>
<dl>
<dt><a href="pruning.html"><code><span data-if="hdevelop" style="display:inline;">pruning</span><span data-if="dotnet" style="display:none;">Pruning</span><span data-if="python" style="display:none;">pruning</span><span data-if="cpp" style="display:none;">Pruning</span><span data-if="c" style="display:none;">pruning</span></code></a></dt>
<dd>Prune the branches of a region.</dd>
</dl>
<dl>
<dt><a href="top_hat.html"><code><span data-if="hdevelop" style="display:inline;">top_hat</span><span data-if="dotnet" style="display:none;">TopHat</span><span data-if="python" style="display:none;">top_hat</span><span data-if="cpp" style="display:none;">TopHat</span><span data-if="c" style="display:none;">top_hat</span></code></a></dt>
<dd>Compute the top hat of regions.</dd>
</dl>
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